Timeline for Why is the Chebyshev function relevant to the Prime Number Theorem
Current License: CC BY-SA 3.0
11 events
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| Jul 19, 2011 at 20:00 | comment | added | Qiaochu Yuan | @David: well, my understanding is that ideas like these feed into Connes' program for proving the Riemann hypothesis. If he succeeds, I imagine that would qualify as evidence... | |
| Jul 19, 2011 at 19:35 | comment | added | David Hansen | @Qiaochu: That's a good point! I meant nothing rude by my remarks - I'd simply like to see some evidence that this is a fruitful point of view, and for me "evidence" means "proofs of desirable theorems". | |
| Jul 19, 2011 at 18:33 | comment | added | Qiaochu Yuan | @David: I don't see why that implies that number theorists shouldn't start thinking like this. Before Riemann, if I told you "perhaps we can prove things about the primes using complex analysis," you could've said the same thing, right? "Forcing a translation into the language of complex analysis is not a motivation. No number theorist has ever thought like this." | |
| Jul 19, 2011 at 18:02 | comment | added | David Hansen | @Qiaochu: Sorry, I'm still not buying it. No number theorist (i.e., the kind of people who prove statistical theorems about the primes) has ever thought like this. | |
| Jul 19, 2011 at 12:39 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Jul 19, 2011 at 12:36 | comment | added | Qiaochu Yuan | @Greg: "forced" seems a little harsh to me. Some people take ideas like these quite seriously, and this exact observation was pointed out by no less a mathematician than Mackey: empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/physics2.htm | |
| Jul 19, 2011 at 9:13 | comment | added | Greg Martin | I truly don't find an explanation involving "Riemann gasses" to be "physically motivated". Forcing a translation into the language of physics is not a motivation. | |
| Jul 19, 2011 at 5:11 | comment | added | Qiaochu Yuan | @David: well, I suppose it is a matter of whether you care about physical intuition or not. The point is that the statistical properties of the Riemann gas should be closely related to statistical properties of the primes. It should be possible to write a complete proof of the PNT in which every step is physically motivated like this but I don't know if anyone's actually done it... | |
| Jul 19, 2011 at 4:52 | comment | added | David Hansen | Partition functions? Riemann gases? Since when do these give "intuitive interpretations" of the zeta function? :) | |
| Jul 19, 2011 at 2:52 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Jul 19, 2011 at 2:13 | history | answered | Qiaochu Yuan | CC BY-SA 3.0 |